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Question

The rate of a first order reaction is 0.04 mol L1min1 at 10 minutes and 0.02 mol L1min1 at 20 minutes. Find the half-life of the reaction (in min).
(Given:ln2=0.693)

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Solution

Let the concentrations of the reactant after 10 minutes and 20 minutes be C1 and C2 respectively.
Rate after 10 minutes=k.C1=0.04 mol L1s1Rate after 20 minutes=k.C2=0.02 mol L1s1
C1C2=0.040.02=2
Let C1C2 be the ratio of initial and final concentrations.
k=110lnC1C2=110ln2
k=110×0.693=0.0693 min1
We know, t12 for a first order reaction is,
t12=0.693k=0.6930.0693=10 min

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